manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4
For percentage questions like this one, it's almost always better to plug in some smart numbers rather than trying to build an equation.
Assume the usual ticket price is $20 (we choose $20 because $20 plus 5% equals $21, an integer, which makes calculations easier). With this price, this month's revenue for 220 tickets would be \(220*$20 = $4,400\), which we are told is 10% greater than the revenue collected previous month. Hence,
previous month's revenue was \(\frac{$4,400}{1.1} = $4,000\).
If the circus were to raise the ticket price by 5%, the new price would be $21. Therefore,
the actual revenue from selling 200 tickets would be \(200 * $21 = $4,200\).
To find out what percent less previous month's revenue would be compared to this month's revenue, we calculate the following: \(\text{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}\%\).
Answer: C.